Is there a way to track my refund without waiving all my rights to privacy and consenting to being monitored?

You asked:  "Is there a way to track my refund without waiving all my rights to privacy and consenting to being monitored?"

Are you referring to a Federal refund and the IRS consent warning that pops up when you attempt to use the "Where's My Refund" tool?

https://www.irs.gov/refunds

I don't know a way to get around that there.    The popup clearly states that the mere use of their system "constitutes consent to monitoring, interception, recording, reading, copying or capturing by authorized personnel of all activities. There is no right to privacy in this system." 

There is another way to check that doesn't require the IRS website.  You can check on your Federal refund by phone using the IRS Refund Hotline.  But it will still ask you for some personal info.  I don't know if it recognizes and records your phone number or not, but I would suspect it does.  I don't know if the recording mentions anything about privacy, rights, etc.  You'll have to see.

800-829-1954

There's also the IRS2Go app which can be downloaded to one's mobile device from links to various app suppliers at the IRS website.  But I would bet since it's from the IRS that that there's some kind of similar consent agreement, terms of use, privacy agreement, etc.  I've never used it, so I don't know what you would encounter in that regard.